Slimness of ellipse secant | Desmos

Expression 6: "T" equals 0

0

360

6

The slimness factor calculation:

7

Expression 8: "F" Subscript, 3 , Baseline equals StartFraction, 2 sin left parenthesis, StartNestedFraction, "t" NestedOver 2 , EndNestedFraction , right parenthesis left parenthesis, "F" Subscript, 0 , Baseline cos squared left parenthesis, "T" plus StartNestedFraction, "t" NestedOver 2 , EndNestedFraction , right parenthesis plus StartNestedFraction, 1 NestedOver "F" Subscript, 0 , Baseline , EndNestedFraction sin squared left parenthesis, "T" plus StartNestedFraction, "t" NestedOver 2 , EndNestedFraction , right parenthesis , right parenthesis Over 1 negative cos left parenthesis, StartNestedFraction, "t" NestedOver 2 , EndNestedFraction , right parenthesis , EndFraction

8

Expression 9: "F" Subscript, 4 , Baseline equals max left parenthesis, "F" Subscript, 3 , Baseline , StartFraction, 1 Over "F" Subscript, 3 , Baseline , EndFraction , 1 , right parenthesis

9

Compare to the slimness of the original ellipse:

10

Expression 11: "y" equals "F" Subscript, 0 , Baseline

equals

10

11

12

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